POST UTME IMS U 2018 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A beam of light passes from air into a glass of re\fractive index $n$. If the angle of incidence is $\theta_i$, find the angle of re\fraction $\theta_r$ u\sing Snell's law.
A. \theta_r = \arc\sin \left\( \frac{n_1 \sin \theta_i}{n_2} \right \)
B. \theta_r = \arc\sin \left\( \frac{n_2 \sin \theta_i}{n_1} \right \)
C. \theta_r = \arc\sin \left\( \frac{n_1 \sin \theta_i}{n_1 + n_2} \right \)
D. \theta_r = \arc\sin \left\( \frac{n_2 \sin \theta_i}{n_1 + n_2} \right \)
Question 2
A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. The capaci\tance is 2.5 nF. If a potential difference of 10 V is applied across the plates, what is the magnitude of the electric field between the plates?
A. 500 V/m
B. 250 V/m
C. 1000 V/m
D. 2000 V/m
Question 3
A particle of mass 0.5 kg is attached to a spring with spring cons\tant 100 N/m. The particle is displaced by 0.2 m from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?
A. 10 rad/s
B. 20 rad/s
C. 5 rad/s
D. 15 rad/s
Question 4
A 50 Hz, 200 V AC supply is connected to a series RLC circuit with R = 10 Ω, L = 0.1 H, and C = 10 × 10^\( -6 \) F. The circuit has a phase angle of 30°. Calculate the impedance of the circuit.
A. ( 15.9 Omega )
B. ( 17.3 Omega )
C. ( 19.7 Omega )
D. ( 21.9 Omega )
Question 5
A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. If the capaci\tance is 8.0 x 10^-10 F, what is the charge on the plates?
A. 4.0 x 10^-10 C
B. 8.0 x 10^-10 C
C. 1.6 x 10^-9 C
D. 3.2 x 10^-9 C
Question 6
A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If the air resis\tance is negligible, calculate the maximum height reached by the projectile.
A. 10.0 m
B. 15.0 m
C. 20.0 m
D. 25.0 m
Question 7
A radioactive sample has an initial activity of 100 Bq. After 2 hours, the activity has decreased to 50 Bq. What is the half-life of the radioactive sample?
A. 1 h
B. 2 h
C. 4 h
D. 8 h
Question 8
A heat engine operates between two reservoirs at temperatures 500 K and 300 K. If the engine absorbs 100 J of heat from the high-temperature reservoir, calculate the efficiency of the engine.
A. 0.25
B. 0.33
C. 0.40
D. 0.50
Question 9
A quantum particle has a wave function given by \( \psi(x) = Ae^{-\alpha x^2} \). If the average value of the position of the particle is 0.5 m, calculate the value of the parameter \( \alpha \).
A. 0.01 m^{-2}
B. 0.05 m^{-2}
C. 0.10 m^{-2}
D. 0.20 m^{-2}
Question 10
A gas is contained in a cylinder of volume $V$ with a movable piston. The gas is heated, cau\sing its pressure to increase from $P_1$ to $P_2$. Find the work done $W$ by the gas u\sing the formula $W = \int_{V_1}^{V_2} P dV$.
A. W = P_2 \( V_2 - V_1 \)
B. W = P_1 \( V_2 - V_1 \)
C. W = \frac{1}{2} \( P_2 + P_1 \) \( V_2 - V_1 \)
D. W = \frac{1}{2} \( P_2 - P_1 \) \( V_2 - V_1 \)
Question 11
A particle of mass $m$ is attached to a spring with spring cons\tant $k$. The particle is displaced by a dis\tance $x_0$ from its equilibrium position and released from rest. Assuming the motion is simple harmonic, find the time $t$ at which the particle's velocity is $v = \frac{dx}{dt} = -omega x_0 \sqrt{1 - \cos^2 omega t}$, where $omega = \sqrt{\frac{k}{m}}$.
A. t = \frac{\pi}{2\omega}
B. t = \frac{\pi}{4\omega}
C. t = \\frac{3\\pi}{4\\omega}
D. t = \frac{\pi}{\omega}
Question 12
A wave has a frequency of 50 Hz and a wavelength of 10 m. Calculate the speed of the wave.
A. \( 500 , \text{m/s} \)
B. \( 600 , \text{m/s} \)
C. \( 700 , \text{m/s} \)
D. \( 800 , \text{m/s} \)
Question 13
A particle moves in a straight line with an initial velocity of 5 m/s and an acceleration of 2 m/s^2. Calculate the velocity of the particle after 4 seconds.
A. \( 9 , \text{m/s} \)
B. \( 10 , \text{m/s} \)
C. \( 11 , \text{m/s} \)
D. \( 12 , \text{m/s} \)
Question 14
A beam of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 30°
C. 40°
D. 50°
Question 15
A light ray passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 30°
C. 40°
D. 50°

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